Investigations in Number, Data, and Space: Teaching Philosophy The Changing Face of Mathematics Instruction: What is different? New roles for teachers and students Teaching for understanding All children can learn Collaborative work Alternative and multiple strategies Organization of the Investigations Curriculum Units (2- 6 weeks) – consists of several investigations on the same/similar topics Investigations several sessions around A set of related problems Math relationships – building/constructing Games about particular mathematics Collecting, representing and interpreting data Sessions – structure/learning cycle Extensions & Excursions - differentiation Learning Cycle ENGAGE (hook; prior knowledge) EXPLORE (hands on; experience) EXPLAIN (term introduction) EXTEND (yet another way) EVALUATE (are learners getting the concept?) If YES, … If NO, … The Mathematics Content Number Data Geometry Change Special Features of the Investigations Curriculum Materials Technology Cooperative learning and grouping Assessment Family connections Review and practice Support for Spanish-speaking students The Teacher’s Role Observe & listen carefully to students; Understand how students are thinking Help students articulate their thinking, verbally & in writing Establish a classroom atmosphere in which high value is placed on thinking hard about a problem Insist that students keep track of their work and be able to explain or show their thinking Ask questions that push students’ mathematical thinking further Facilitate discussions about important math ideas Make decisions about how to modify the curriculum appropriately for individuals or groups of students Differentiating Instruction: Can we do it? Everybody Counts (NRC, 1989) Investigating real-life contexts Linguistically diverse classroom Spanish vocabulary package Tips for linguistically diverse classroom Family letters (in six languages) Investigating mathematical contexts Differentiating Instruction: Process standards Problem solving Communication Connections Reasoning and proof Representations

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# Investigations in Number, Data, and Space: …